There is but it doesn't feel its a legit job. Coz if you think logically,why don't the company send the email themself?
I think there are already so many email companies that it's really not possible to to kind of believe in the legitimacy of such offers. And to be frank, I've not yet heard of any company that is offering this sort of thing.
I don't think any such service exists. I have heard about "get paid to read mails" but not "get paid to write mails"